Preheat waffle iron on high until just beginning to smoke. Reduce heat to moderate and brush generously with some butter. Spread butter on 1 side of 8 bread slices and turn slices over. Top 4 slices with 1 slice ham and 1 slice cheese, folding in any overhang, and then top with remaining 4 buttered bread slices, buttered sides up. Cook sandwiches in batches (number of batches will depend on size of your waffle maker) until bread is golden and crisp, 4-6 minutes. Assemble and cook 4 more sandwiches in same manner. Just before serving, cut each sandwich into 2 triangles.